News broke on Sunday that the couple -- who got engaged in June after less than a month of dating -- have split. According to our source, the pair broke up due to bad timing. Grande is still dealing with the death of her ex-boyfriend, rapper Mac Miller, in September from an apparent overdose. The two are also, of course, busy with their thriving careers.

“Ariana made the final decision," the source says. "It was time to realize this wasn’t the right time for them and Pete is incredibly heartbroken. Pete is still so in love with her. He wanted his whole world to revolve around her but she was emotionally unavailable. He realizes she was at her limit with pressure from everyone and everything around her. There were days she just wanted to run away from the world just to get some peace and quiet and peace of mind. Pete had to give her that space out of love."

On Saturday, 25-year-old Grande canceled a scheduled performance at F**k Cancer’s inaugural Barbara Berlanti Heroes fundraising gala, where her manager, Scooter Braun, noted to the attendees that she "needs this time." According to our source, Grande's loved ones support her decision to take a step back from her relationship.

“Ariana and Pete didn’t plan this abrupt split, but they both know this breakup is the right decision for them right now," the source says. "Their family and friends stand behind their decision entirely and Ariana’s team feels this will give her time to heal."

“They got engaged because they both felt this instant connection and even now after their split they are still deeply in love," the source continues of Grande and Davidson. "But their timing has truly affected their plans and made it impossible for them to make it work at the moment. ... They have a very special connection, partly because Pete has been there for Ariana during a painful time in her life. She will forever and always be grateful to Pete."

“They felt constantly under a microscope," the source says. "They felt that they literally had no privacy and it really took a toll on their relationship."

Still, the source says that the two are still very much in touch -- and are definitely not ruling out the possibility of getting back together. A separate source says Grande was backstage with 24-year-old Davidson just this past Saturday night at Saturday Night Live and was affectionate with him.

“They have not stopped talking since they made the decision to split and in fact they plan on trying to stay close friends or maybe one day even more than that," the source says. “They are remaining positive and looking forward to a future together where they may be best friends and still haven’t ruled out the possibility of one day making their relationship work."

“They just know that they cannot be engaged right now or be in a serious relationship because of the stress Ariana has had to face recently and the stress of their careers," the source continues. "Pete’s acting career has taken off. He signed on to so many projects and feature films and Ariana has a huge album to promote. And they just barely have time for that. They want to make sure if they ever do decide one day to make it work that they make their relationship a priority. They both want a family one day and realize they will have to step back a bit from their careers to do that. They love and trust each other so much and want to keep the option open for a further together."